New variable separation approach: application to nonlinear diffusion equations

The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach. As a consequence, a complete list of canonical forms for such equations which admit the derivative-dependent functional separable solutions is obtained and some exact solutions to the resulting equations are described.Comment: 19 pages, 2 fig

Conservation laws for self-adjoint first order evolution equations

In this work we consider the problem on group classification and conservation laws of the general first order evolution equations. We obtain the subclasses of these general equations which are quasi-self-adjoint and self-adjoint. By using the recent Ibragimov's Theorem on conservation laws, we establish the conservation laws of the equations admiting self-adjoint equations. We illustrate our results applying them to the inviscid Burgers' equation. In particular an infinite number of new symmetries of these equations are found and their corresponding conservation laws are established.Comment: This manuscript has been accepted for publication in Journal of Nonlinear Mathematical Physic

Peculiarities of electronic heat capacity of thulium cuprates in pseudogap state

Precise calorimetric measurements have been carried out in the 7 - 300 K temperature range on two ceramic samples of thulium 123 cuprates TmBa2Cu3O6.92 and TmBa2Cu3O6.70. The temperature dependence of the heat capacity was analyzed in the region where the pseudogap state (PGS) takes place. The lattice contribution was subtracted from the experimental data. The PGS component has been obtained by comparing electronic heat capacities of two investigated samples because the PGS contribution for the 6.92 sample is negligible. The anomalous behavior of the electronic heat capacity near the temperature boundary of PGS was found. It is supposed that this anomaly is due to peculiarities in N(E) function where N is the density of electronic states and E is the energy of carriers of charge.Comment: 12 pages, 3 Postscript figure

Gene transfer using new complexes between cardiolipin-like dicationic lipids and plasmid DNA to tumor cells

The lipid vesicles of bisamphiphiles cardiolipin-like dicationic lipids (CDL) I-IV were studied for creation of lipoplexes with plasmid DNA of different sizes to obtain stable lipoplexes for gene transfer to gene therapy. Lipoplexes' sizes (300±100 nm) and stablity (> 2 hrs) of CDL were sufficient to be used in gene transfer against monolayer and suspension cell cultures. The CDL total cytotoxicity determined by MTT-test was lower compare to lipofectin as a control. Transfection conditions against tumor cells lines were optimized by lipoplexes of CDL and plasmid DNA. The most efficient transfection for lipoplexes CDL-plasmid DNA was at the lipid-DNA (L/D) ratio equal to 5 (for lipofectin, it was 2). For monolayer cell cultures, lipoplexes CDL-I are comparable in terms of transfection efficacy with lipofectin; in the case of suspension culture, their efficiency was lower by one order of magnitude. It permits a usage of lipoplexes suggested as mediators for gene transfer and delivery to human tumor cells

Non-Arrhenius Behavior of Surface Diffusion Near a Phase Transition Boundary

We study the non-Arrhenius behavior of surface diffusion near the second-order phase transition boundary of an adsorbate layer. In contrast to expectations based on macroscopic thermodynamic effects, we show that this behavior can be related to the average microscopic jump rate which in turn is determined by the waiting-time distribution W(t) of single-particle jumps at short times. At long times, W(t) yields a barrier that corresponds to the rate-limiting step in diffusion. The microscopic information in W(t) should be accessible by STM measurements.Comment: 4 pages, Latex with RevTeX macro

The interplay of intrinsic and extrinsic bounded noises in genetic networks

After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a genetic network. The influence of intrinsic and extrinsic noises on genetic networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: $(i)$ the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, $(ii)$ a model of enzymatic futile cycle and $(iii)$ a genetic toggle switch. In $(ii)$ and $(iii)$ we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possibile functional role of bounded noises

Dust density waves in a dc flowing complex plasma with discharge polarity reversal

We report on the observation of the self-excited dust density waves in the dc discharge complex plasma. The experiments were performed under microgravity conditions in the Plasmakristall-4 facility on board the International Space Station. In the experiment, the microparticle cloud was first trapped in an inductively coupled plasma, then released to drift for some seconds in a dc discharge with constant current. After that the discharge polarity was reversed. DC plasma containing a drifting microparticle cloud was found to be strongly non-uniform in terms of microparticle drift velocity and plasma emission in accord with [Zobnin et.al., Phys. Plasmas 25, 033702 (2018)]. In addition to that, non-uniformity in the self-excited wave pattern was observed: In the front edge of the microparticle cloud (defined as head), the waves had larger phase velocity than in the rear edge (defined as tail). Also, after the polarity reversal, the wave pattern exhibited several bifurcations: Between each of the two old wave crests, a new wave crest has formed. These bifurcations, however, occurred only in the head of the microparticle cloud. We show that spatial variations of electric field inside the drifting cloud play an important role in the formation of the wave pattern. Comparison of the theoretical estimations and measurements demonstrate the significant impact of the electric field on the phase velocity of the wave. The same theoretical approach applied to the instability growth rate, showed agreement between estimated and measured values.Comment: 7 pages, 4 figure

Finite Volume Kolmogorov-Johnson-Mehl-Avrami Theory

We study Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory of phase conversion in finite volumes. For the conversion time we find the relationship $\tau_{\rm con} = \tau_{\rm nu} [1+f_d(q)]$. Here $d$ is the space dimension, $\tau_{\rm nu}$ the nucleation time in the volume $V$, and $f_d(q)$ a scaling function. Its dimensionless argument is $q=\tau_{\rm ex}/ \tau_{\rm nu}$, where $\tau_{\rm ex}$ is an expansion time, defined to be proportional to the diameter of the volume divided by expansion speed. We calculate $f_d(q)$ in one, two and three dimensions. The often considered limits of phase conversion via either nucleation or spinodal decomposition are found to be volume-size dependent concepts, governed by simple power laws for $f_d(q)$.Comment: 4 pages, 4 figures. Additions after referee reports: Scaling of the variable q is proven. Additional references are adde

Morphology of supported polymer electrolyte ultra-thin films: a numerical study

Morphology of polymer electrolytes membranes (PEM), e.g., Nafion, inside PEM fuel cell catalyst layers has significant impact on the electrochemical activity and transport phenomena that determine cell performance. In those regions, Nafion can be found as an ultra-thin film, coating the catalyst and the catalyst support surfaces. The impact of the hydrophilic/hydrophobic character of these surfaces on the structural formation of the films has not been sufficiently explored yet. Here, we report about Molecular Dynamics simulation investigation of the substrate effects on the ionomer ultra-thin film morphology at different hydration levels. We use a mean-field-like model we introduced in previous publications for the interaction of the hydrated Nafion ionomer with a substrate, characterized by a tunable degree of hydrophilicity. We show that the affinity of the substrate with water plays a crucial role in the molecular rearrangement of the ionomer film, resulting in completely different morphologies. Detailed structural description in different regions of the film shows evidences of strongly heterogeneous behavior. A qualitative discussion of the implications of our observations on the PEMFC catalyst layer performance is finally proposed